Reflected Brownian Motions in the KPZ Universality Class

• Main Authors: Weiss, Thomas (Author), Ferrari, Patrik (Author), Spohn, Herbert (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: SpringerBriefs in Mathematical Physics, 18
• Subjects: Physics.; Probabilities.; Mathematical physics.; Statistical Physics and Dynamical Systems.; Mathematical Physics.; Probability Theory and Stochastic Processes.

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, be...

Table of Contents:

• Introduction
• One-sided reflected Brownian motions and related models
• Skorokhod construction
• Packed initial conditions
• Infinite particle systems
• Determinantal point processes
• Definition
• Fredholm determinants
• Correlation kernel
• Strategy for future proofs.-Airy processes.-Elementary Airy processes
• Crossover Processes
• Variational identities
• Gaussian fluctuations of the Airy_stat process
• Packed and Periodic initial conditions
• Packed initial conditions
• Periodic initial conditions
• Stationary initial conditions
• Poisson initial conditions
• Determinantal structure
• Asymptotic analysis
• Path-integral style formula
• Analytic continuation
• More general initial conditions and their asymptotics
• Half-Periodic initial conditions
• Half-Poisson initial conditions
• Poisson-Periodic initial conditions
• Attractiveness and a more general class of initial data
• Asymptotics along space-like paths and slow decorrelations
• References.